The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X
 0 X^2+2  0 X^2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0 X^2  0 X^2 X^2  2 X^2  2  2  2 X^2+2 X^2+2 X^2  2 X^2+2  0 X^2  2  2 X^2 X^2  0 X^2+2  2  0 X^2  2 X^2 X^2+2  2 X^2+2  0 X^2+2 X^2 X^2+2 X^2+2  2  0  2
 0  0 X^2+2 X^2  0 X^2+2 X^2  0  0 X^2+2 X^2  0  0 X^2+2 X^2  0  2 X^2+2 X^2  2 X^2+2  0  0 X^2  2 X^2+2 X^2+2  2  2 X^2+2 X^2  2  0 X^2  2 X^2+2  0  2 X^2+2 X^2+2 X^2  2  2 X^2+2 X^2  2  2  2  2  2 X^2+2 X^2 X^2 X^2 X^2
 0  0  0  2  0  0  2  0  2  2  0  2  2  2  0  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  2  2  2  0  0  2  2  2  0  0
 0  0  0  0  2  2  2  2  2  2  0  2  0  0  2  0  0  0  0  0  2  2  2  2  0  0  0  0  2  2  2  2  2  2  2  2  0  0  2  0  2  2  0  0  0  2  0  2  2  0  0  2  0  0  2

generates a code of length 55 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+61x^52+120x^54+640x^55+155x^56+40x^58+6x^60+1x^108

The gray image is a code over GF(2) with n=440, k=10 and d=208.
This code was found by Heurico 1.16 in 3.38 seconds.